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Figure 5. DISCUSSION QUESTION: The mode 6 seems rather over represented. Can you think of any explanation for this, or is it just chance. It is interesting to ask what kind of a probability model would be appropriate to describe the time between winning the jackpot. The probability of the jackpot being won depends on the number of tickets sold. (Actually, on the number of different picks chosen.) If the same number of tickets were sold on each drawing then the appropriate model would be: toss a coin with probability p for heads until the first time heads turns up where 1/p is the average time between heads. Unfortunately, it is not at all reasonable to assume the same number of tickets will be sold. Here is what the Powerball FAQ says about this: For a $10 million jackpot draw we sell about $11 million. For a $20 million jackpot we sell about $13 million. With a $100 million jackpot we sell $50 to $70 million for the draw (depending on time of year and other factors). Let's assume that, for a particular jackpot, n million tickets are sold. Then the probability that a particular person does not win the jackpot is b–1 where, for the old version of the game, b = 45 × C(45,5) = 54,979,155. b The probability that none of the tickets sold wins the jackpot is (b–1 )n . b 20PDF Image | USING LOTTERIES IN TEACHING A CHANCE COURSE
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